Lemma 6.41 (See [1]}.) 
 Referring to Notation REF ,
let \(M \in \text{\rm Mat}_{d+1}(\mathbb {F})\)  represent \(A\)  with respect to a basis of \(V\)  that
satisfies Definition REF (i).
Then
\(M_{i,i} &= a_i \qquad (0 \le i \le d),&M_{i, i-1} M_{i-1,i} &= x_i \qquad (1 \le i \le d).\) 

